Final answer:
The current that results in a magnetic dipole moment of magnitude 2.04 A⋅m² for a circular coil of 167 turns and radius 1.72 cm is approximately 0.0067 A.
Step-by-step explanation:
The magnetic dipole moment of a circular coil is given by:
μ = nIA
where μ is the magnetic dipole moment, n is the number of turns, I is the current, and A is the area of the coil.
We are given that the coil has 167 turns and a radius of 1.72 cm. The area of the coil can be calculated using the formula for the area of a circle:
A = πr²
Substituting the given values, we have:
A = π(0.0172 m)²
Now we can calculate the current I using the formula for magnetic dipole moment:
μ = nIA
Substituting the given values, we have:
2.04 = (167)(I)(π(0.0172 m)²)
Solving for I, we find that the current that results in a magnetic dipole moment of magnitude 2.04 A⋅m² is approximately 0.0067 A.